<!DOCTYPE html>
<html lang="en-US">
<!--********************************************-->
<!--*       Generated from PreTeXt source      *-->
<!--*                                          *-->
<!--*         https://pretextbook.org          *-->
<!--*                                          *-->
<!--********************************************-->
<head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<meta name="robots" content="noindex, nofollow">
</head>
<body class="ignore-math">
<h3 class="heading"><span class="type">Paragraph</span></h3>
<p>The general solution is</p>
<div class="displaymath process-math" data-contains-math-knowls="">
\begin{equation*}
{\bf x}=C_1 \left(\begin{array}{c}
1\\
1
\end{array}\right)  e^{-t}+C_2 \left(\begin{array}{c}
1\\
-1
\end{array}\right)  e^{-3t},
\end{equation*}
</div>
<p class="continuation">i.e.,</p>
<div class="displaymath process-math" data-contains-math-knowls="">
\begin{equation*}
x_1=C_1 e^{-t}+C_2 e^{-3t},\quad
x_2=C_1 e^{-t}-C_2 e^{-3t}.
\end{equation*}
</div>
<span class="incontext"><a href="sec6_2.html#p-261" class="internal">in-context</a></span>
</body>
</html>
